APPENDIX B
REAL ESTATE FORMULAS: SUMMARIZING THE ESSENTIALS
Accelerated Depreciation
(B ÷ P) * R = D
where:
B |
= basis of asset |
P |
= period (in years) |
R |
= acceleration percentage |
D |
= annual depreciation |
Accumulated Value of 1
(R + 1)n * P = A
where:
R |
= periodic interest rate |
n |
= periods |
P |
= principal amount |
A |
= amount accumulated (principal plus interest) |
Accumulated Value of 1 per Period
[D [(1 + R )n – 1] ÷ R] * P = A
where:
D |
= periodic deposit amount |
R |
= periodic interest rate |
n |
= number of periods |
P |
= principal |
A |
= accumulated value of 1 per period |
Adjusted Basis in Property
P + C – D = B
where:
P |
= purchase price |
C |
= closing costs |
D |
= deferred gain |
B |
= basis in property |
Adjusted Purchase Price
P + C = A
where:
P |
= purchase price |
C |
= closing costs |
A |
= adjusted purchase price |
Adjusted Sales Price
S – C = A
where:
S |
= sales price |
C |
= closing costs |
A |
= adjusted sales price |
After-Tax Cash Flow
[R – (E + D)] – [P + C – T ] = CF
where:
R |
= rental income |
E |
= cash expenses |
D |
= depreciation |
P |
= principal payments |
C |
= capital expenditures |
T |
= income tax savings |
CF |
= after-tax cash flow |
Amortization Payment
B (1 ÷ Pn) = A
where:
B |
= original balance of the loan |
P |
= present value of 1 per period |
n |
= number of periods |
A |
= amount of payment per period |
(R + 1)y = i
where:
R |
= interest rate |
y |
= number of years |
i |
= accumulated interest |
Annual Percentage Rate
[(i ÷ P) + 1]n – 1 = R
where:
i |
= annual interest rate |
P |
= number of periods |
n |
= number of periods per year |
R |
= annual percentage rate |
Annualized Return (Using Months)
(R ÷ H) * 12 = A
where:
R |
= return over entire holding period |
H |
= holding period (number of months) |
A |
= annualized return |
Annualized Return (Using Years)
R ÷ H = A
where:
R |
= return over entire holding period |
H |
= holding period (number of years) |
A |
= annualized return |
Area of a Circle
π * r2 = A
where:
π |
= pi |
r |
= radius |
A |
= area of a circle |
Area of a Square or Rectangle
L * W = A
where:
L |
= length |
W |
= width |
A |
= area |
Area of a Trapezoid
[(b1 + b2) / 2] * a = A
where:
b1 |
= base number 1 |
b 2 |
= base number 2 |
a |
= altitude |
A |
= area of a trapezoid |
Area of a Triangle
(b * a) ÷ 2 = A
where:
b |
= base |
a |
= altitude |
A |
= area of a triangle |
Assessment Ratio
A ÷ P = R
where:
A |
= assessed value |
P |
= asked price |
R |
= assessment ratio |
Balance Sheet
A = L + N
where:
A |
= assets |
L |
= liabilities |
N |
= net worth |
Bank Reconciliation
(C ± E) = A
(B + T – O ± E) = A
where:
C |
= checkbook balance |
E |
= errors |
A |
= reconciled balance |
B |
= bank statement balance |
T |
= deposits in transit |
O |
= outstanding checks |
Breakeven After Taxes and Inflation
I ÷ (100 – E) = B
where:
I |
= inflation rate |
E |
= effective tax rate |
B |
= breakeven after taxes and inflation |
(O + M) ÷ G = R
where:
O |
= operating expenses |
M |
= mortgage debt service |
G |
= effective gross income |
R |
= breakeven ratio |
Capital Gain or Loss
(S – Cs) – L + D – (P – Cp – G) = N
where:
S |
= sale price |
Cs |
= closing costs at sale |
L |
= carryover losses |
D |
= depreciation claimed |
P |
= purhase price |
Cp |
= closing costs at purchase |
G |
= deferred gains |
N |
= net capital gain or loss |
Capitalization Rate
I ÷ P = C
where:
I |
= annual net income |
P |
= purchase price |
C |
= capitalization rate |
Carryover Loss Allocation
L ÷ T = A
where:
L |
= loss reported for the property |
T |
= total net loss, all properties |
A |
= allocation percentage |
Cash Income
N ÷ D = C
where:
N |
= net income |
D |
= depreciation expense |
C |
= cash income |
Cash-on-Cash Return
C ÷ I = R
where:
C |
= annual cash flow |
I |
= cash investment |
R |
= cash-on-cash return |
Checking Account Math Verification
E + C – D = P
where:
E |
= ending balance |
C |
= checks |
D |
= deposits |
P |
= previous balance |
Closing Prorated Days (Buyer)
R – D = P
where:
R |
= days remaining as of prior month end |
D |
= days in partial month |
P |
= prorated days, buyer |
Closing Prorated Days (Seller)
U + D = P
where:
U |
= days used as of prior month end |
D |
= days in partial month |
P |
= prorated days, seller |
Closing Prorated Interest
(( L * I ) ÷ D) * (D ÷ M )) = P
where:
L |
= loan amount |
I |
= interest rate |
D |
= days of prorated interest |
M |
= days in the month |
P |
= prorated interest |
Closing Prorated Property Taxes
T * (D ÷ L) = P
where:
T |
= total property tax bill, half-year |
D |
= days of responsibility |
L |
= days in liability period |
P |
= prorated property taxes |
Conversion, Acres to Square Feet
A * 43,560 = F
where:
A |
= acres |
F |
= square feet |
I ÷ 12 = F
where:
I |
= inches |
F |
= feet |
Conversion, Percentage to Decimal
R ÷ 100 = D
where:
R |
= interest rate |
D |
= decimal equivalent |
Conversion, Square Feet to Acres
F ÷ 43,560 = A
where:
F |
square feet |
A |
= number of acres |
Conversion, Yards to Feet
Y * 3 = F
where:
Y |
= yards |
F |
= feet |
Cost Approach
C – D + L = V
where:
C |
= cost of improvements |
D |
= depreciation |
L |
= land value |
V |
= value of the property |
Cost of Financed Property
( P*M ) + D = C
where:
P |
= monthly payment |
M |
= number of months in loan term |
D |
= down payment |
C |
= total cost of property |
Current Ratio
A ÷ L = R
where:
A |
= current assets |
L |
= current liabilities |
R |
= current ratio |
Current Yield (Bond)
N ÷ P = Y
where:
N |
= nominal yield |
P |
= premium or discount |
Y |
= current yield |
Current Yield (Stock)
D ÷ P = Y
where:
D |
= dividend per share |
P |
= current price per share |
Y |
= current yield |
Daily Compounding
R ÷ 365 = i
where:
R |
= annual interest rate |
i |
= daily rate |
Debt Coverage Ratio
I ÷ M = R
where:
I |
= net operating income |
M |
= mortgage payment |
R |
= debt coverage ratio |
Debt-to-Equity Ratio
D ÷ (D + E) = R
where:
D |
= long-term debt |
E |
= equity |
R |
= debt capitalization ratio |
Depreciation (Appraisal)
100 ÷ E = D
where:
E |
= economic life |
D |
= annual rate of depreciation |
Depreciation Basis (Appraised Value)
I ÷ V = A
where:
I |
= improvement value per appraisal |
V |
= total appraised value |
A |
= allocated basis, improvements |
Depreciation Basis (Assessed Value)
I ÷ V = A
where:
I |
= improvement value per assessment |
V |
= total assessed value |
A |
= allocated basis, improvements |
Depreciation Basis (Insured Value)
L ÷ V = A
where:
L |
= insurance limits of liability, dwelling |
V |
= total basis in the property |
A |
= allocated basis, improvements |
Discount Yield
(A – P) ÷ A = Y
where:
A |
= appraised value |
P |
= asked price |
Y |
= discount yield |
Double-Entry Bookkeeping, Basic Formula
D = C
where:
D |
= balance of all debit-balance accounts |
C |
= balance of all credit-balance accounts |
Economic Rent per Room
R ÷ N = E
where:
R |
= rent per period |
N |
= number of rooms |
E |
= economic rent per room |
Economic Rent per Square Foot
R ÷ S = E
where:
R |
= rent per period |
S |
= square feet |
E |
= economic rent per square foot |
Economic Rent per Unit
R ÷ U = E
where:
R |
= rent per period |
U |
= number of units |
E |
= economic rent per unit |
Equity
V – B = E
where:
V |
= current market value |
B |
= balance, mortgage debt |
E |
= equity |
Equity Dividend Yield
C ÷ D = Y
where:
C |
= net cash flow |
D |
= down payment |
Y |
= equity dividend yield |
Equity Return
(C + P) ÷ D = R
where:
C |
= cash income |
P |
= principal reduction |
D |
= down payment |
R |
= equity return |
Estimated Monthly Payment
(Pa + Pb) ÷ N = A
where:
Pa |
= payment, higher interest rate |
Pb |
= payment, lower interest rate |
N |
= number of rates |
A |
= average |
[( M – P) – O] ÷ P = C
where:
M |
= current market value |
P |
= fixed option price of the property |
O |
= option cost |
C |
= exercise cost |
Exercise Return (to Tenant)
O ÷ (M – P) = R
where:
O |
= option cost |
M |
= current market value |
P |
= fixed option price of property |
R |
= exercise return |
Expense Allocation (Even Distribution)
E ÷ P = A
where:
E |
= nonspecific expenses |
P |
= number of properties |
A |
= allocation percentage |
Expense Allocation (Months Owned)
M ÷ T = A
where:
M |
= months of ownership during the year |
T |
= total months of ownership, all properties |
A |
= allocation percentage |
Expense Allocation (Prepayments)
E ÷ M = A
where:
E |
= total prepaid expense |
M |
= number of months the expense relates to |
A |
= allocation amount |
Expense Allocation (Revenue Share)
R ÷ T = A
where:
R |
= revenue received for the property |
T |
= total revenue, all properties |
A |
= allocation percentage |
Expense Allocation (Square Feet)
F ÷ T = A
where:
F |
= rentable square feet, each unit |
T |
= total square feet, all units |
A |
= allocation percentage |
Expense Ratio
E ÷ I = R
where:
E |
= operating expenses |
I |
= gross income from rents |
R |
= expense ratio |
Exponential Moving Average
{[(V1 + V2 . . . Vf) ÷ N] – L} * (2 ÷N) + [(V1 + V2 . . . Vf) ÷ N] = NA
where:
V |
= values in the selected field |
V |
= 1, 2, . . . f = first, second, remaining, and final values |
N |
= number of values in the field |
L |
= latest entry |
NA |
= new moving average |
Floor-Area Ratio
B ÷ L = F
where:
B |
= building area |
L |
= land area |
F |
= floor-area ratio |
Gross Rent Multiplier
S ÷ R = G
where:
S |
= sales price |
R |
= rent per period |
G |
= gross rent multiplier |
Half-Year Convention
B ÷ 2 = H
where:
B |
= basis of the asset |
= half-year depreciation base, first-year |
Income Statement
R – ( C + E ) = N
where:
R |
= revenues |
C |
= costs |
E |
= general expenses |
N |
= net profit or loss |
Loan-to-Value Ratio
L ÷ V = R
where:
L |
= loan balance |
V |
= value (sales price or appraisal) |
R |
= ratio |
Loss Ratio
N ÷ G = L
where:
N |
= nonrentable area |
G |
= gross building area |
L |
= loss ratio |
Market or Sales Comparison Approach
(C1 + C2 + . . . Cn ± A) ÷ N = V
where:
C |
= comparable property values |
1, 2, . . . n |
= comparable properties |
A |
= plus or minus adjustments |
N |
= number of comparable values |
V |
= market value |
Math Check, Change in Loan Balance
PB – NB = P
where:
PB |
= previous balance |
NB |
= new balance |
P |
= principal payments |
Math Check, Interest/Principal
P + I = T
where:
P |
= principal amount |
I |
= interest amount |
T |
= total of payments |
Maximum Loss Allowance
$25,000 – ((A – $100,000) ÷ 2) = L
where:
A |
= adjusted gross income |
L |
= maximum loss allowed |
Mid-Month Convention
(B ÷ 24) * P = M
where:
B |
= basis of the asset |
P |
= number of half-month periods |
M |
= mid-month depreciation basis, first year |
Monthly Compounding
R ÷ 12 = i
where:
R |
= interest rate |
i |
= monthly rate |
Monthly Loan Amortization
P – [T (P * ( i ÷ 12))] = N
where:
P |
= previous balance, mortgage loan |
T |
= total payment |
i |
= interest rate |
N |
= new balance, mortgage loan |
Months of Property Inventory on the Market
I ÷ S = M
where:
I |
= total inventory of properties currently available |
S |
= average sales per month |
M |
= months of inventory currently available |
(V1 + V2 + . . . Vf) ÷ N = A
where:
V |
= values in the selected field |
1, 2, . . . f |
= first, second, remaining, and final values |
N |
= number of values in the field |
A |
= moving average |
Net Current Value of Property
C – (C * R * E) = N
where:
C |
= cost |
R |
= rate of depreciation |
E |
= effective age |
N |
= net current value |
New Basis in 1031 Exchange
P – D = N
where:
P |
= adjusted purchase price |
D |
= deferred gain |
N |
= new basis |
Occupancy Rate
O ÷ T = R
where:
O |
= occupied units |
T |
= total units |
R |
= occupancy rate |
Operating Expense Ratio
E ÷ I = R
where:
E |
= operating expenses |
I |
= rental income |
R |
= operating expense ratio |
Option to Exercise Ratio
O ÷ S = R
where:
O |
= option price |
S |
= sale price upon exercise |
R |
= ratio |
Partial Month’s Rent Liability
D ÷ M = P
where:
D |
= days in period to be counted |
M |
= full month |
P |
= partial month liability |
Payback Ratio
I ÷ C = R
where:
I |
= cash investment |
C |
= net cash flow |
R |
= payback ratio |
Periodic Rate
R ÷ P = i
where:
R |
= annual interest rate |
P |
= number of periods |
i |
= periodic interest rate |
Pi
C ÷ D = π
where:
C |
= circumference of a circle |
D |
= diameter of a circle |
π |
= value of pi, 3.1416 |
Present value of 1
1 ÷ (1 + R)n= P
where:
R |
= periodic interest rate |
n |
= periods |
P |
= present value factor |
Profit Margin
C ÷ I = P
where:
C |
= cash flow |
I |
= effective gross income |
P |
= profit margin |
Prorated Rent, Partial-Year Use
R ÷ F = P
where:
R |
= rental period |
F |
= full year |
P |
= prorated rent |
Prorated Rent, Tenant Share
T ÷ F = P
where:
T |
= tenant’s square-foot share |
F |
= total square feet |
P |
= prorated rent |
Quarterly Compounding
R ÷ 4 = i
where:
R |
= interest rate |
i |
= quarterly rate |
Rate of Return
(V – C) ÷ C = R
where:
V |
= current value (or sales price) |
C |
= original cost or basis |
R |
= rate of return |
Return on Equity
(P-B) ÷ (B÷Y) = R
where:
P |
= proceeds upon sale |
B |
= basis |
Y |
= years held |
R |
= return on equity |
Return on Investment
(P – O) ÷ O = R
where:
P |
= proceeds upon sale |
O |
= original investment |
R |
= return on investment |
Return on Rental Income
N ÷ I = R
where:
N |
= net profit |
I |
= rental gross income (revenues) |
R |
= return on rental income |
Rule of 69
(69 ÷ i) + 0.35 = Y
where:
i |
= interest rate |
Y |
= years required to double |
Rule of 72
72 ÷ i = Y
where:
i |
= interest rate |
Y |
= years required to double |
Rule of 113
113 ÷ i = Y
where:
i |
= interest rate |
Y |
= years required to triple |
Semiannual Compounding
R ÷ 2 = 1
where:
R |
= interest rate |
i |
= semiannual rate |
Simple Interest
P * R = I
where:
P |
= principal |
R |
= interest rate |
I |
= interest |
Sinking Fund Payments
1 ÷ [( 1 + R )n ÷ R] = S
where:
R |
= periodic interest rate |
n |
= number of periods |
S |
= sinking fund factor |
(SP – AP) ÷ AP = S
where:
SP |
= sale price |
AP |
= asked price |
S |
= spread |
Straight-Line Depreciation
B ÷ P = D
where:
B |
= basis of asset |
P |
= period (in years) |
D |
= annual depreciation |
Tax Benefits from Reporting Losses
E * L = S
where:
E |
= effective tax rate |
L |
= net loss from real estate |
S |
= savings from reduced taxes |
Total Return
(C + I + T) ÷ Y = R
where:
C |
= capital gains |
I |
= total net income |
T |
= net tax benefit (or cost) |
Y |
= years held |
R |
= total return |
Trial Balance
(A – L – N) = P
(R – C – E) = P
where:
A |
= asset account balances |
L |
= liability account balances |
N |
= net worth account balances |
P |
= profit (or loss) |
R |
= revenue account balances |
C |
= cost account balances |
E |
= expense account balances |
Vacancy Rate
V ÷ T = R
where:
V |
= vacant units |
T |
= total units |
R |
= vacancy rate |
Volume of a Cylinder
π * r2 * H = V
where:
π |
= pi |
r |
= radius |
H |
= height |
V |
= volume |
Volume of a Rectangular Solid
L * W * H = V
where:
L |
= length |
W |
= width |
H |
= height |
V |
= volume |
Weighted Average Interest Rate
[(L1 * R1) + (L2 * R2)] ÷ Lt = A
where:
L1 |
= balance, loan 1 |
L2 |
= balance, loan 2 |
Lt |
= total balances of loans |
R1 |
= rate on loan 1 |
R2 |
= rate on loan 2 |
A |
= average interest rate |
Weighted Moving Average
(V1 + V2 + . . . (Vf * 2)) ÷ (N + 1) = A
where:
V |
= values in the selected field |
1, 2, . . . f |
= first, second, remaining, and final = values |
N |
= number of values in the field |
A |
= weighted moving average |
Working Capital
A – L = W
where:
A |
= current assets |
L |
= current liabilities |
W |
= working capital |